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James_Miller comments on If there IS alien super-inteligence in our own galaxy, then what it could be like? - Less Wrong
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Not necessarily - See Hilbert's Paradox.
https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
If an infinite number of aliens have the potential to make contact with us (which I realize isn't necessarily implied by your comment) then some powerful subset must be shielding us from contact.